This is an analysis of analyses. The Rind et al. team
did not add a new study of a new sample to the existing ones. Meta-analysis is a
method to review the data and the results of existing studies. The method makes
it possible to compare the data and the results of many other studies and to
'add' the data and the results together, so to speak. By this method, all
samples together form a 'new' big sample. This is the strength of a
meta-analysis. A statistical rule is: the greater the sample, the more the
results can be trusted.

Correlation is the central concept in the study.
Correlation is the association between two or more factors. A factor or a
moderator is a force that may have some influence (e.g., intelligence can
influence school results). A factor has to be measured by some method. The
outcome of the measurement is a variable (e.g., an intelligence
quotient).

If a researcher measures the I.Q. of a sample of children,
the I.Q. figures will vary among the children. The result of the
measurement will show the variability of the sample.

With some methods, one can estimate the variability of the population
(e.g. all children of a given age in a given country). Then it's called the
population variance.

Analysis of variance or ANOVA, like correlation,
measures the association between two or more factors. Put another way,
correlation and ANOVA measure how variability in one variable is related to
variability in another variable.

The level of correlation is reflected in a correlation
coefficient, noted as r, a figure between +1.00 (the longer it rains,
the more water in a bin) and -1.00 (the more it rains, the lower the amount of
children playing on the streets). The significance (credibility) of this figure
depends on the size of the sample, thus on the amount of observations or
participants. The more observations for a given value of r, the more
significance. Therefore, the number of participants is usually given after the r
with the letter n or N.

Note that the size of the association between two variables
(i.e., r) is a different concept than statistical significance,
which addresses the question of whether or not the two variables are really
related to one another. For the meta-analysis, r is used as a measure of effect
size.

In a meta-analysis, most of the correlation coefficients are
given after a correction in which the size of the sample is included in the
calculation. After doing so, a more unbiased r appears: the ru. This
figure reflects the best estimate of the level of the correlation within the
population.

One useful property of r is that the figure r
or rucan be squared. This figure is named the ‘coefficient
of determination’ or ‘percentage of variance accounted for’. If some
variable V1 predicts 50% of the variability in some variable V2, then the
coefficient of determination would be .50 (which corresponds to an r of
about .7). Note, that 0.9 x 0.9 = 0.81 and that 0.4 x 0.4 = 0.16. The squared
figure ru2 is lower than the ru.

To interpret the effect size, the Rind team calls an r=.50
large, .30 medium, and .10 small. Thus a coefficient of determination of 1% is
small, 9% is medium, and 25% is large.

The main factor in the meta-analysis is the experience of
CSA. This main factor is compared with many other factors, for example
adjustment and many psychological factors. If there appeared to be a high
percentage of variance between CSA and, say, adjustment, one supposes that the
CSA experience had a (small, medium, or large) effect on the adjustment.
If the degree of consent or the gender appears to have effect on the
adjustment, than the degree of consent or the gender can be seen as a
moderator.

Because the studies gave one effect size for each sample, the
number of effect sizes is the same as the number of samples, mentioned in the
tables as k.

As it has been said: the greater the sample, the more
reliable is the correlation. To give a measure for the reliability, usually two
figures are given; the one lower and the other higher than the computed
correlation coefficient. Between these two figures, the correlation is reliable
with a chance of 95% - or a chance of 2.5% that the correlation is lower than
the lowest figure and 2.5% that it's higher than the highest figure.

Note that, if the first figure is below zero and the latter
above zero, the correlation can be negative as well as positive. If both figures
are above zero, we know (with a confidence of 95%) that there is a positive
correlation between the given figures, but if one of the figures is zero or
negative, we can’t even say with sufficient confidence wether the correlation
is negative or positive. This, to cite page 29 of the meta-analysis, "an
interval not including zero indicated an effect size estimate was
significant."

If the researcher is quite sure that the correlation will be
a positive one (as in the example of the wet streets and the rain), he tests
only at the positive side of the possible correlation coefficients. This is a
one-tailed test. If the researcher is not sure of how two variables are
related, or if he wants to know the size of the correlation rather than just its
existence or non-existence, he should test at both ends of the possible
correlation coefficients: he does a two-tailed test.

This is the correlation between several symptoms (for
example, depression) and the CSA factor, as it appeared in all samples in which
these symptoms are measured. The CSA factor usually has two levels: with
or without CSA experience. In other studies, more levels are used, e.g. contact
CSA, non-contact CSA, no CSA. The ‘without-group’ is the control group. If,
say, 50% of the CSA group had depressive symptoms and also 50% of the control
group had depressive symptoms, the effect size of CSA will be zero. If 100% of
the CSA group had these symptoms and 0% of the control group, the correlation
and the effect size would be 1.00.

This correlation reflects the overall association between CSA
and those types of adjustment measured in the several samples, corrected for the
sample size. If a study measured four symptoms in one sample, these four
symptom-level effect sizes in the study are averaged into one sample-level
effect size in the meta-analysis.

A meta-analysis combines the data from several studies about
the same subject. Homogeneity measures the differences or similarities
between the several studies. If several studies reach nearly the same
conclusion, one can combine the data with reasonable confidence. If the studies
differ greatly in their outcomes, one should be more cautious about combining
the data. The statistical measure of homogeneity between the outcomes of the
studies has been given in the tables as H.

This H is calculated by a test, named
"Chi-square" that compares the differences between groups of data. The
more groups of data, the higher the Chi square will be. The statistical way of
saying this is "df (degrees of freedom) = k (number of
choices or groups) – 1". To know the significance of the
chi-square, one has to look at a table. Usually, the significance is mentioned
as an (*) in the tables. An asterisk means that the groups of data were
different, a non-significant H suggusts that there was a great deal of
homogeneity amongst the several studies. The asterix is explained in the tables
as "p < .05 in chi-square test." This means that the cance
that such great differences between homologous data would occur is smaller than
5%. To reach homogeneity, the authors removed the most extreme effect sizes,
irrespective of wether they were extremely high or extremely low, until
homogeneity was reached – if possible. Otherwise, the studies could not be
compared with on another with confidence.

Suppose that five studies resulted in the following effect
sizes: 0.14, 0.17, 0.23, 0.25 and 0.27. The mean effect size (neglecting the
sample size in this example) is 0.21. Now suppose a sixth study resulted in an
effect size of 0.70. Then, the mean will be 0.29. The one high effect size will
raise the mean and the sixth study would have great influence on the results. It
is better to expel this sixth study from the meta-analysis since it seems to be
an aberration. These kinds of studied are called "outliers".

Factually, three studies were outliers: two studies with very
high positive effect sizes (having many incest cases in the samples) and one
with a negative effect size. "Positive" should be read as: "the
more CSA, the more problems with adjustment – see page 31 of the
meta-analysis.

If one has a set of effect sizes, one can compute the mean
effect size. It is better to include the size of the sample in the computation.
Doing so, the larger samples have more influence on the mean than the smaller
samples. This mean is called a weighted mean.

A correlation coefficient r or ru is
not an interval measure: i.e. the distance between r = 0.1 to r =0.2
is not the same as the distance from r = 0.8 to r = 0.9. A
transformation to Fisher's Z gives each correlation coefficient a figure that
better reflects its position in the collection of all coefficients when
performing meta-analyses. It makes it possible to use the correlation
coefficient and the sample size in a calculation of the weighted mean. This
weighted mean can then be transformed back into a correlation coefficient.

The standard deviation is a figure, mostly between –
2.0 and 2.0, that shows the position of each of the data in the total collection
of data. Data with a SD of 0.0 are the mean data. About half of the data have
positions between SD – 0.1 and 0.1. Data with positions like – 1.9 or 1.9
are at the extremes of the data collection.

This is a method to compare several ('multiple') factors and
to compute the strength of the influence of each of them on another factor. This
kind of analysis is better than the 'simple correlation' between only two
variables.

Take for example the learning process at school. We can
suppose that several factors have influence: the intelligence of the children,
the method of teaching, the size of the classes and the personality of the
teacher. If you have enough data, you can take the data of the children of the
same teacher, the same intelligence and the same class size but with a different
method of teaching. Then you 'regress' all factors except one. So you can
see if the method of teaching has any influence by computing the correlation
between that one factor and the regressed other factors. This correlation is
called a partial correlation. With the regression of fewer other factors,
it's called a semi partial correlation. By making many of these
comparisons, you're doing multiple analysis to compute the strength of
each factor. Remember that in the meta-analysis, the factor 'family environment'
and 'CSA experience' together had influence on the adjustment, but that
'family environment' appeared to have 10 times more influence than the factor
"CSA experience".